|
| 1 | +""" |
| 2 | +Filename: lqnash.py |
| 3 | +Authors: Chase Coleman, Thomas Sargent |
| 4 | +
|
| 5 | +This file provides an example of a Markov Perfect Equilibrium for a |
| 6 | +simple duopoly example. |
| 7 | +
|
| 8 | +See the lecture at http://quant-econ.net/markov_perfect.html for a |
| 9 | +description of the model. |
| 10 | +
|
| 11 | +""" |
| 12 | +from __future__ import division |
| 13 | +import sys |
| 14 | +import numpy as np |
| 15 | +import scipy.linalg as la |
| 16 | +import matplotlib.pyplot as plt |
| 17 | +from numpy import sqrt, max, eye, dot, zeros, cumsum, array |
| 18 | +from numpy.random import randn |
| 19 | +from quantecon.lqnash import nnash |
| 20 | + |
| 21 | + |
| 22 | +#---------------------------------------------------------------------# |
| 23 | +# Set up parameter values and LQ matrices |
| 24 | +# Remember state is x_t = [1, y_{1, t}, y_{2, t}] and |
| 25 | +# control is u_{i, t} = [y_{i, t+1} - y_{i, t}] |
| 26 | +#---------------------------------------------------------------------# |
| 27 | +a0 = 10. |
| 28 | +a1 = 1. |
| 29 | +beta = 1. |
| 30 | +d = .5 |
| 31 | + |
| 32 | +a = eye(3) |
| 33 | +b1 = array([[0.], [1.], [0.]]) |
| 34 | +b2 = array([[0.], [0.], [1.]]) |
| 35 | + |
| 36 | +r1 = array([[a0, 0., 0.], |
| 37 | + [0., -a1, -a1/2.], |
| 38 | + [0, -a1/2., 0.]]) |
| 39 | + |
| 40 | +r2 = array([[a0, 0., 0.], |
| 41 | + [0., 0., -a1/2.], |
| 42 | + [0, -a1/2., -a1]]) |
| 43 | + |
| 44 | +q1 = array([[-.5*d]]) |
| 45 | +q2 = array([[-.5*d]]) |
| 46 | + |
| 47 | + |
| 48 | +#---------------------------------------------------------------------# |
| 49 | +# Solve using QE's nnash function |
| 50 | +#---------------------------------------------------------------------# |
| 51 | + |
| 52 | +f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0., 0., 0., 0., 0., 0., |
| 53 | + tol=1e-8, max_iter=1000) |
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